The dynamics of multi-layer transducer systems are modelled and simulated by use of a multi-domain spectral method. The model accounts for a nonlinear constitutive relation between the electric displacement and the electric field. Simulation of resonance and wave propagation in the transducer is implemented using a domain-decomposition method and governing equations in each layer are discretized using a Chebyshev collocation method. The model is applied to a reciprocal transducer system, as used in many engineering applications including ultrasonic flowmeter applications and blood-velocity measurement setups, where the transducer consists of a PZT5 piezoceramic layer and a matching layer. © 2008 Elsevier Inc. All rights reserved.
Wang, L., & Willatzen, M. (2009). Modelling of nonlinear dynamics for reciprocal multi-layer piezoceramic transducer systems. Applied Mathematical Modelling, 33(5), 2263–2273. https://doi.org/10.1016/j.apm.2008.06.003